That works, and is better than putting it all on one staff, but I would prefer a standard tremolo indication, which might make it clearer that you want each group to end with the auxiliary and not with the principal tone, if that is indeed what you want. Pianists have to make a judgement call about the ending note of a trill. Individual trills are assumed to end with the principal note, but chains of trills as in your example can go either way depending on what sounds best.

And the stems can all be up, since you are not actually beaming between the staves, and the trill symbol is best over each of the notes

About the tremolo: later on the principal trill notes will be of shorter values and diverse rhythms, resulting in a more complex picture of tremolos, therefore I've chosen tr instead.
Also I have chosen stems to be "intendedly" connecting; also because I have later on eight notes with connected beams. But, maybe these 8-notes should not be cross-staffed? EDIT: In that case the rests should be shown.

But good that nothing else was more awkward here: I was very curious about single stave version.

If you put it all on one staff, the right hand would have the stems up and the left hand stems down and the position of the trill symbols would be as you show them in your example. No rests would be necessary or desirable.

If you feel that it shows the melodic connection better to stem it as shown on two staves, that is certainly your perogative as the composer. But it would not be considered necessary given the slur.

I'm curious whether you want the trills to end with the auxiliary or with the principal note. It is ambiguous as it stands and a conscientious performer might inquire.